Find the distance between the lines $5x + 12y + 13 = 0$ and $5x + 12y - 9 = 0$.

The length of the perpendicular from the point $(a \cos \alpha, a \sin \alpha)$ to the line $y = x \tan \alpha + c, c > 0$ is .....

Let the angles made with the positive x-axis by two straight lines drawn from the point $P(2,3)$ and meeting the line $x+y=6$ at a distance $\sqrt{\frac{2}{3}}$ from the point $P$ be $\theta_{1}$ and $\theta_{2}$. Then the value of $(\theta_{1}+\theta_{2})$ is:

The number of points on the line $x+y=4$ which are at a unit distance from the line $2x+2y=5$ is

Find the distance between the parallel lines $l(x + y) + p = 0$ and $l(x + y) - r = 0$.

If the length of the perpendicular drawn from the point $(4,1)$ to the line $3x - 4y + k = 0$ is $2$ units,then the values of $k$ are: